Recent advances in conformal field theory and critical phenomena have focused on the characterization of boundary or defects in a conformally invariant system. In this Letter, we study the critical behavior of the three-dimensional Ising universality class in the presence of a surface, realizing the ordinary, the special, and the normal universality classes. By combining high-precision Monte Carlo simulations of an improved model, where leading scaling corrections are suppressed, with a finite-size scaling analysis informed by conformal field theory, we determine unbiased, accurate estimates of universal boundary operator product expansion coefficients of experimental relevance. Furthermore, we improve the value of the scaling dimension of the surface field at the special transition by the estimate Δ ̂ σ = 0.3531 ( 3 ) .
We study the special point in the phase diagram of a semi-infinite system where the bulk transition is in the three-dimensional Ising universality class. To this end we performed a finite-size-scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interaction. In order to check for the effect of leading bulk corrections we also simulated the spin-1/2 Ising model on the simple cubic lattice. We accurately estimated the surface enhancement coupling at the special point of these models. We find
yt1=0.718(2) and
yh1=1.6465(6) for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.
We study the boundary critical behavior of the three-dimensional Heisenberg universality class, in the presence of a bidimensional surface. By means of high-precision Monte Carlo simulations of an improved lattice model, where leading bulk scaling corrections are suppressed, we prove the existence of a special phase transition, with unusual exponents, and of an extraordinary phase with logarithmically decaying correlations. These findings contrast with naïve arguments on the bulk-surface phase diagram, and allow us to explain some recent puzzling results on the boundary critical behavior of quantum spin models.
Using Monte Carlo methods and finite-size scaling, we investigate surface criticality in the
O(n) models on the simple-cubic lattice with
n=1, 2, and 3, i.e., the Ising,
XY, and Heisenberg models. For the critical couplings we find
Kc(n=2)=0.4541659 (10) and
Kc(n=3)=0.693003 (2). We simulate the three models with open surfaces and determine the surface magnetic exponents at the ordinary transition to be
yh1(o)=0.7374(15), 0.781 (2), and 0.813 (2) for
n=1, 2, and 3, respectively. Then we vary the surface coupling
K1 and locate the so-called special transition at ${\ensuremath{\kappa}}_{\mathrm{c}}(n=1)=0.502\phantom{\rule{0.2em}{0ex}}14$ (8) and ${\ensuremath{\kappa}}_{\mathrm{c}}(n=2)=0.6222$ (3), where $\ensuremath{\kappa}={K}_{1}∕K\ensuremath{-}1$. The corresponding surface thermal and magnetic exponents are
yt1(s)=0.715 (1) and
yh1(s)=1.636 (1) for the Ising model, and
yt1(s)=0.608 (4) and
yh1(s)=1.675 (1) for the
XY model. Finite-size corrections with an exponent close to $\ensuremath{-}1∕2$ occur for both models. Also for the Heisenberg model we find substantial evidence for the existence of a special surface transition.